A company that makes a peer to peer protocol to send encrypted messages where the key comes from multiple clients (and each client will not send the piece after the expiration date) is going to make money.
This has nothing at all do to with an erasable internet. You've described a system where someone has a time limit to view information, and if they fail to view it then it's destroyed. Anything that can be seen or heard can also be copied, so once it's decrypted and visible it no longer matters that there's a time limit.
Some firm that uses decent cryptography will make a mint just assuring people that a conversation has a high chance of staying stays private and vanishing after it was done.
This is not possible. You do not have control over the recipient's system so there is no way to ensure it's actually erased. It doesn't matter how much encryption or protection you use on a message. Once it's decrypted it's out of your control and the recipient, or anyone with control over the receiving device, can do anything they want with it. Even if you did create an easy to use system of encryption, those keys would be stolen and shared just like passwords are.
We are each entitled to our own opinion, but no one is entitled to his own facts. -- Patrick Moynihan